02719nam a22003975i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001400153072001700167072002300184072001600207100008600223245008200309250001800391264007200409300004400481336002600525337002600551338003600577347002400613490004600637505033300683520102501016650002802041650002802069710003402097773002602131776003602157776003602193830004602229856004602275978-981-97-3984-4DE-He21320251030112623.0cr nn 008mamaa240711s2024    si |    s    |||| 0|eng d  a97898197398447 a10.1007/978-981-97-3984-42doi 4aQA370-380 7aPBKJ2bicssc 7aMAT0070002bisacsh 7aPBKJ2thema1 aCoclite, Giuseppe Maria.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aScalar Conservation Lawsh[electronic resource] /cby Giuseppe Maria Coclite.  a1st ed. 2024. 1aSingapore :bSpringer Nature Singapore :bImprint: Springer,c2024.  aXIV, 148 p. 20 illus.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aSpringerBriefs in Mathematics,x2191-82010 aChapter 1 Introduction -- Chapter 2 Entropy Solutions -- Chapter 3 Riemann Problem -- Chapter 4 Functions with Bounded Variation -- Chapter 5 Wave Front Tracking -- Chapter 6 Vanishing Viscosity -- Chapter 7 Compensated Compactness -- Chapter 8 Periodic solutions -- Chapter 9 Oleinik Estimate -- Chapter 10 Lax-Oleinik Formula.  aThis book are notes prepared for the PhD courses that the author has been teaching during the last 10 years. The material available in the already existing literature (papers and essays) has been collected in this unique text, presenting the results with all the details for the reader’s convenience, fixing a unified notation, and providing a consistent framework for the subject. These notes cover many of the arguments that usually can be found in high level essays, where the proofs are simply sketched, and in papers, which are not easily available and not always self-contained. This book is intended for 1. PhD students in Mathematics, Physics and Mechanical Engineering in order to learn the basic features of nonlinear scalar equations, 2. researchers interested in nonlinear hyperbolic PDEs in order to learn the details behind some known and deep results on nonlinear scalar equations, 3. teachers of courses on nonlinear PDEs. The readers are expected to know the basic measure theory and Sobolev spaces. . 0aDifferential equations.14aDifferential Equations.2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978981973983708iPrinted edition:z9789819739851 0aSpringerBriefs in Mathematics,x2191-820140uhttps://doi.org/10.1007/978-981-97-3984-4